This is the recipe I have used for years to critical acclaim.
HOT AND SOUR S0UP
4 dried mushrooms
1-2 T ground black pepper
2 squares fresh bean curd
2 T cider vinegar
1⁄2 cup bamboo shoots
3 T cornstarch (dissolved in cold water)
1⁄4 lb pork, may add more
1 qt chicken stock
1 egg lightly beaten
1 T soy sauce
1⁄4 cup tiger lily buds (golden needles)
1⁄4 cup wood ears (cloud ears)
2 t sesame oil
1 scallion, minced
1. Soak the dried mushrooms, wood ears, and golden needles in hot water until soft, about 1⁄2 hour. Then remove stems from mushrooms and cut into large shreds. Divide golden needles lengthwise in half by hand. Slice wood ears. Reserve soaking liquid.
2. Shred bean curd, pork, and bamboo shoots.
3. Combine in pot the stock, soaking liquid, soy sauce, mushrooms, bamboo shoots, golden needles, pork, and wood ears. Bring to a boil over high, heat. Then immediately reduce the heat to low and cover the pot and simmer for 5 minutes.
4. Then drop in the bean curd, pepper, and vinegar. Bring to boil again.
5. Add some soup to the cornstarch mixture to warm it, and then pour it into the soup. Stir until the soup thickens. If it doesn’t within a minute or so, just add more cornstarch paste.
6. When thickened, slowly pour in the beaten egg, stirring in a figure-eight pattern all, the time to avoid lumps
7. Just before serving, add sesame oil and sprinkle with scallions.
NOTE: It is important in this dish to have an equally strong flavor of vinegar and pepper. Keep adding either until you are satisfied with the tartness and spiciness.
I'm not sure what your aversion is to cornstarch; however, it is one of the most common thickeners used in Asian, and frankly, most cuisines. You're basically making a slurry, so you can use arrowroot... and I suppose flour. Flour will most likely just impart a flavor you might not want to have in the soup.
Without the thickening agent, the soup will just be runny. It won't really alter the taste, but it just won't have an ideal consistency.
I would say hot and sour can still be pretty darned good without the tiger lily buds, but rarely does it not have shitakes, wood ears, and the bean curd/hard tofu.
It also often has thin slivers of bamboo, which come in cans at an Asian store but which I've never looked for at a megachain.
I used this recipe from the The Chinese Cookbook, by Craig Claiborne and Virginia Lee, but with my modifications:
"Hot and Sour Soup"
5-6 cups rich chicken stock, preferably home made.
4-6 dried Chinese black mushrooms or shiitakes
2 large tree mushrooms (wood ears)
6 tiger lily stems
1/2 cup shredded raw lean pork
1 TBSP light soy sauce
1/2 cup shredded bamboo shoots
salt to taste
2-3 TBSPS white vinegar (The book specifies red wine vinegar, but I prefer white)
1tsp dark soy sauce
2 TBSPS cornstarch
3 TBSPS cold water in which to suspend the cornstarch
1 1/2 pads fresh beancurd, sliced into thin strips. (Nowadays, one shelf stable box of Mori-nu brand Firm Tofu is sufficient or even excessive.)
2-3 whole eggs, beaten
1 tsp ground white or black pepper (I prefer the extra kick of black)
1TBSP Oriental sesame oil
2 TBSPS chopped or shredded green onions, including the green part
Minced fresh coriander (cilantro--optional) for garnish.
Place dried vegetables in a bowl and pur boiling water over. Soak 15-20 minutes.
Rinse off mushrooms. Remove hard stems,, then shred with a kife. Set aside.
Next, rinse off the hydrated tree fungus and remove any woody parts. Shred similar to mushrooms.
Remove hard bud from end of tiger lily stem, shred lengthwise with fingers, Set aside.
Mix shredded pork with the light soy sauce and stir fry briefly in 1TBSP veg oil . (I say, this step is optional). Add the bamboo shoots, mushrooms, tree fungus and tiger lily stems and stir fry briefly. Add the chicken stock, vinegar and salt.
Allow to come to a boil, then lower heat to a simmer.
Combine the corstarch and water and stir into the simmering mixture. When slightly thickened, add the bean curd/tofu. Bring to a boil, then turn off heat for about 30 seconds so as not to curdle the eggs when added.
Add the sesame oil and pepper and blend.
Pour into a hot soup tureen.
Gradually stir in the eggs in a circular motion. Sprinkle with the shredded scallion/green onion and the optional cilantro.
This is similar to the one I make. You can leave out the lily buds, bamboo shoots and tree mushrooms, but dried shitakes are essential for the flavor of the recipe. However, if you can't find dried shitakes, it might be interesting to sub another dried mushroon with a really intense flavor. Maybe not authentic but I'll be it's delish!